As discussed in detail in SI-16, we compute the thermopower and resistivity as a function of filling and temperature for the model of Ref.[1]} using Hartree-Fock (HF) approximation. The model consists of four spin-valley flavors, interacting with local Coulomb interaction \(U\) . For the results reported in the main text, we have taken \(U=1.2 W\) , where \(W\)  is the band width of the conduction (valence) band. The HF self-consistency equations depend on the non-interacting DOS of the moire' flat bands. We use various non-interacting DOSs, e.g. DOSs obtained from the continuum Bistritzer-MacDonal model [2]} in Ref. [1]} and the DOS generated from the continuum model of Ref. [4]}, which includes lattice relaxation effects. The self-consistent HF DOS is then used to compute thermopower and resistivity via Kubo formulae neglecting vertex corrections. We assume a constant band velocity and use a small impurity scattering rate \(\Gamma _0=0.001W\)  in the Kubo formulae.
